If you’re running macOS, try opening the TIFF in Apple Preview. If that works, you can export to a file format that Photoshop will open (you can drag and drop to the Desktop or a folder as well). If the TiFF has layers, I have found drag and drop to be the quickest way to get the them into PS.
I am getting the same error.
I have just created 3 HDR images using Photoshop's Merge to HDR Pro feature and saved them as 32-bit TIFFs.
The first one opens OK, but the other 2 give the error "Could not complete the request because it is not the right kind of document."
Photoshop CS6 on Windows 7-64